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Educational Studies in Mathematics

, Volume 82, Issue 1, pp 75–96 | Cite as

Intuiting the fundamental theorem of arithmetic

  • Martin GriffithsEmail author
Article

Abstract

Our aim here was to explore, via a specific instance, the potential for learners to develop mathematically as a consequence of the interplay between intuition and indirect classroom experience rather than through explicit tuition. A significant aspect of this study is the recognition of the possibility for learners to be able to thematize schemata associated with the fundamental theorem of arithmetic without formal knowledge of either the theorem or its consequences. Our findings would suggest that some learners, by way of a series of key intuitive episodes or concrete classroom experiences, do indeed possess the capacity to create meaningful mathematical structures that, though perhaps imperfectly formed, may in some sense mirror schemata.

Keywords

Algebraic structure Fundamental theorem of arithmetic Intuition Multiplicative structure Schema 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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